?9O0?30 101 '> · disclaimer notice this document is best quality practicable. the copy furnished...
109
........ ....... .................................. ............. S/• • :TECHNICAL REPORTh• . -. . .. . ... . ioo :~~ .n/ . - TkADCOM SIGNAL ANALYSIS PROGRAU (9 )EPu10inft&78 17 4 LL I by G. A./• .1. a, M 7 90: ,-7. 0. .. G.. 1 ... ixi,,.f .* , / ,/4' " ' / :, Approved £f0cr public release, j distribution unlimited. Iaa aIIIII~ l I l ImIIl Il I l ( IIl U.S. ARMY TANK-.AUTOMOTIVE ' / RESEARCH AND DEVELOPMENT COMMAND Warren, Michigan 48090 ?9O0?30 101 '> _ _ _ _ _ _ _ _ _ _ / a, ' - - *-~.~nI
Transcript of ?9O0?30 101 '> · disclaimer notice this document is best quality practicable. the copy furnished...
........ ....... .................................. .............
S/• • :TECHNICAL REPORTh•... -. ... .... ..
ioo
:~~ .n/ .-TkADCOM SIGNAL ANALYSIS PROGRAU
(9 )EPu10inft&78
17 4
LL I
by G. A./• .1.
a, M
7 90: ,-7. 0.
.. G.. 1 ... ixi,,.f
.* , / ,/4' " ' /
:, Approved £f0cr public release,
j distribution unlimited.
Iaa aIIIII~ l I l ImIIl Il I l ( IIl
U.S. ARMY TANK-.AUTOMOTIVE ' /
RESEARCH AND DEVELOPMENT COMMANDWarren, Michigan 48090?9O0?30 101 '>
_ _ _ _ _ _ _ _ _ _ /
a, ' - - *-~.~nI
DISCLAIMER NOTICE
THIS DOCUMENT IS BEST QUALITYPRACTICABLE. THE COPY FURNISHEDTO DDC CONTAINED A SIGNIFICANT
NUMBER OF PAGES WHICH DO NOTREPRODUCE LEGIBLY.
/
ABSTRACT
This report describes an integrated package for evaluatingterrain data on the Tektronix 4014 graphics terminals on thePicatinny Arsenal CDC 6500/6600 time sharing system. Theprogram provides the following options: first-to-lastpoint detrending, digital high-pass filter, exponentiallyweighted running average, no detrending, interpolation,amplitude smoothing, and a GEO window. Terrain data inputto the program may be used during processing, rather thanthe data equations that are contained in the program. Graphicsdisplays include a linear plot of e'levation vs. distance,a point plot of amplitude vs. period, and a log-log graphof power spectral density vs. frequency. The model structure,with its capabilities and its limitations, is included alongwith user instructions for running the program.
:;' 07 30 101I Px
TABLE OF CONTENTS
Abstract ............. ................... iiIntroduction ......... ............. . . . 1Objective ............ ................... 2TSAP Running Instructions ....... ........... 3TSAP Sample Output p t... ........... 13TSAP Input Data. . . ......... . .... ......... .. 19TSAP Listing ........ ........... 20TSAP Variable Index. . . . ....... ............ 41TSAP Glossazy .............................. 52,TSAP Flowchart ........... .............. .. 56Appendix I Terrain Characterization ........ ... 91Distribution List ....... ............... ... 103DD Form 1473 ........... ................. .104
I
iii
4
INTRODUCTION
The TARADCOM Signal Analysis Program (TSAP) was developed
originally as a BASIC Wang Program by Mr. Robert Daigle ofStevens Institute of Technology and Zoltan J. Janosi of theApplied Research Function of the Survivability ResearchDivision, DRDTA-ZS. The TSAP was converted from BASIC toFORTRAN so as to facilitate running the program in a morecommonly known language on the CDC 6500/6600 time sharingsystem. The following graphics displays were added at thetime of conversion: a linear plot of elevation vs. distance,a point plot of amplitude vs. period and a log-log graph ofpower spectral density vs. frequency.
--- o -
OBJECTIVE
The objective of this report is to provide a user manualfor the TARADCOM Signal Analysis Computer Program with listingsof the program, variables, glossary, and flowchart, andinstructions for input, output, and running the program.
I.I,
,2
!,
I',
RUNNING INSTRUCTIONSFOR
THE SIGNAL ANALYSIS PROGRAM
The following page is a copy of the Tektronix screen
showing the interactive command instructions and system
responses for running TSAP. After all of the instructions
(shown in lower case) have been input, the screen will clear
and processing will proceed. Terminal user responses to
programmed questions are used as input to TSAP and are the
basis for the selection of the available options. The
eight questions with possible answers are on page 57-60
After all of the questions have been answered, the screen
clears and processing continues.
After the output is finished, the terminal user should
key in the following:
BATCH, TEKLD42, LOCAL
E,TEKLD42,S
At this point TEKLD42 is no longer a remote output file. If the
same program is to be used, it may be saved at this time. The
user should also discard the fi js created earlier in the
terminal session; e.g., in this case C45 should be discarded.
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6 -.9, 6.9 6.99 7.00 6.99 7.04 7.07 7.07 7.10 7.123411- 7.12 7.14 7.12 7.11 7.10 7.06 7.{(2 7.00 6.95 6.89G,= 6.,4 8.82 6.79 6.73 6.72 6.72 6.69 6.66 6.68 6.68I1,1: 6.4I 6.71 6.71 6.72 6.76 6.80 6.82 6.87 6.87 6.87I.N= 6.G9 6.91 6.90 6.9:3 6.93 6.96 7.00 7.03 7.0 3 7.061:'= 7.06 7.0:3 (.1:5 7. 08 7'.06 7.07 7.04 6.99 7.01 6.991 6,. .91' 6.95 6.93 6.89 6.88 6.88 6.84 6.83 6.83 6.83I', 3.• b 6.81 6.82 6.81 6.78 6.82 6.82 6.81 6.81 6.82£10= 6.83 6.85 6.90 6.90 6.90 6.93 6.94 6.934 6.95 6.92L' I= 6.92 6.96 6.94 6.91 6.93 6.94 6.91 6.9. 6.92 6.8963i, . 6.83 6.78 6.73 6.72 6.70 6.73 6.74 6.73 6.71, 6.72 6.71 6.71 6.73 6.74 6.73 6.72 6.75 6.73 6.71G"= 6.74 6.I 7 6.73 6.77 6.76 6.75 6.7e 6.81 6.81 6.83C..,I 7.8 G 6.88 6.88 6.91 6.91 6.91 6.94 6.99 6.98 7.0427o= 7.05 7.02 7.07 7.13 7.12 7.13 7.17 7.13 7.13 7.16L'8* 7.17 7.17 7.22 7.22 7.22 7.24 7.2e. 7.26 7. 25 7.23
7 '.23 7.28 7.30 7.28 7.28 7.29 7.30 7.23 7. P9 7.32.'. : ,= 7.3.3 7.35 7. 38 7.41 7.39 7.39 7. 40 7.4-1 7'.4a 7.44":I I" 7.44 7.47 7.49 7.48 7.50 7.54 7.55 7.53 7.57 7.572 ,' 7.60 7.69 7.73 7.75 7.79 7.84 7.84 7.08 7.92 7.967.93 7.9.." :'.95 7.97 7.96 7.95 7.95 7.94 7.93 7.8904 , .88 7.85 7.79 7.80 7.81 7.81 7.80 7.81 7.86 7.357:-88:; . 7 .4' 90 7.90 7.94 7.95 8.00 0.02 8.04 8.10
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I, 10.67 10.68 10.69 10.69 10.71 10.75 10.78 10.79 10.88. 10.8851,• 10.86 10.85 10.84 10.80 10.81 10.75 10.71 10.70 10.67 10.63':,/ 10.66 10.70 10.71 10.74 10.77 10.80 10.82 10.85 10.86 10.88
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U)A ,x - %C43, L&. 1-0, 0 1.
tr0 to*Z-I-+4A7 0rI; jLaa - 0 .4 -C%
w1 ad,~ .40 0 Z 4 ~ - * Z- X 0-7 * ra -
I U.1 CL 2 .C C'% Z f - Q *06L Z C )I AC- A u u
*0-. In I 9'HH
0 C c c
In U)
399
c 0 ccic ao 0 0 cc 0
% ~ ~ C ok f-I - CýfP- e.~t ?- P- P-fl l-
c C c cc c 0 c0 c0 c cc c
44*
4.4
Ln v 0I- $A, W
0..-4 4* c 01
UJ * cIX c t-X Ac C
a o -- - X U v .- 0
44
INDEX OF VARIABLES FOR SIGNAL ANALYSIS PROGRAM(VARIABLE NAME AND PROGRAM LINE NUMBERS)
A 483q. 5090, 5370, 5400, 5420, 5490,5890, 6000. 6030,. 6060, 6110
AAZ 7260, 7270
AZ 7260, 7270, 7280
ANSI 180, 320, 330, 340, 350, 360, 370, 860,960, 1410, 1420, 1860, 1870, 3550,3610, 3720, 4130, 4230, 5330, 6700,7000, 716Q0, 7380, 7730
ANS2 41.0, 420, 430, 870, 970, 990, 1200, 18804960, 5130, 5550, 6030, 6080, 6150,7410
ANS3 180, 470, 480, 490, 880, 1040, 1050,1070
ANS4 180, 540, 550, 560, 890, 1010, 1100,1630, 2110, 7110, 7260
ANS5 180, 600, 610, 620, 900, 1140, 1400
ANS6 180, 660, 670, 680, 910, 1470, 2060
ANS7 180, 720, 730, 740, 920
ANS8 180, 780, 790, 800, 930, 5780
Al(,) 130, 1190, 1290, 1310, 1680, 1840,1920, 2020, 2230, 2330, 2360, 2370,2380, 2390. 2620, 2640, 2710, 2760,3080, 3090, 3930, 3940, 3980, 4000,4030, 4060, 4390, 4400, 4410, 4480,4580, 4640, 4680, 4700, 4890, 5040,5050, 5170, 5990, 6480, 6490, 6500,6560, 6620, 6740, 6760, 6780, 6800,6860, 6870, 6890, 6980, 7080, 7190,7240, 7690, 7700
41
A2(,) 130, 1310, 1690, 3090, 393G, 3940,3990, 4010, 4030, 4060, 4420, 4430,4440, 4490, 4590, 4600, 4650, 4660,4670, 4690, 4710, 5040, 5050, 6000,7090, 7520, 7580, 7620, 7680, 7690,7700
B 6000, 6020
Bl 2380, 2400, 2490, 2510, 2540, 2630,2750
B2 2390, 2400, 2630, 2640, 2690, 2700,2740, 2750, 2760, 2780, 2790, 2820
B3 2630, 2650
B4 2640, 2650
C 6610, 6620, 6630
CCl 6580, 6590, 6600
CC2 6590, 6600, 6630
t CC3 6600, 6630
Co 190, 1160 1170, 1180, 1220, 1230,1290, 1310, 1660,. 1670, 1680, 1690,1790, 1800, 1840, 2280, 2290, 2330,2600, 2610, 2620, 2640, 2710, 2760,3010, 3020, 3080, 3090, 5970, 5980,5990, 6000, 6400, 6410, 6480, 6840,6850, 6860, 6870, 6890, 6980, 7030,7040, 7080, 7090, 7220, 7230, 7240,
7500, 7510, 7520, 7690, 7700
CZ 4530, 4590, 4610, 4630, 4650, 4670
42
i
Cl 190, 1820, 1830, 1840, 1940, 1950,2020, 3040, 3050, 3090, 4460, 4470,4480, 4490, 4540, 4550, 4580, '4590,4600, 4610, 4640, 4650, 4660, 4680,4690, 6430, 6440, 6490, 7060, 7070,7080, 7560, 7570, 7580, 7660, 7670,7680, 7690, 7700
C2 190, 1970, 1980, 2020, 3060, 3070,3080, 4560, 4570, 4580, 4590, 4600,4610, 4640,-4650, 4660, 4670, 4700,4710, 6470, 6480, 6510, 7610, 7620,7630
C3 190, 2000, 2010, 2020, 6540, 6550,
6560
D 7380, 7430, 7450, 7700
E •970, 980, L020
"�' F 4860, 4 9 7 04 5200, 5280, 5300, 5380, '5400, 5420, 5440, 6100, 6110, 6120
pI 4020, 500, 5280, 5480
G 5130, 5170, 5180, 5190, 5310, 5320,5400, 5420, 5450, 6040, 6050, 6110,6130, 6140
GO() 5990, 6000
1 1120, 1190, 1210, 1780, 1790, 1800,1810, 2960, 3010, 3020, 3030, 3340,3410, 3420, 3430, 3440, 3450, 3520,3720, 3840, 3950, 3860, 3950, 3960,3970, 40301 4060, 4230, 4910, 4950,4960, 5010, 5020, 5260, 5330, 5340,'5360, 5370. 5380, 5390, 5440, 5450,5500, 5870, 5910, 6070, 6080, 6110,6120, 6380, 6390, 6420, 6450, 6520,6530, 6600, 6610, 6830, 6840, 6850,7020, 7030, 7040, 7050, 7400, 7410,
7420
43
|h0
IA 7180, 7190
IB 7170, 7180, 7190
IE 980, 1640, 7400, 7410, 7480, 7490,7540, 7660
i0 1610, 1620, 1640, 2270, 2280, 2290,2480, 2490, 2510, 2530, 2550, 2590,2600, 2610, 2690, 2700, 2720, 2730,6390, 6400, 6410, 7210, 7220, 7230,7240, 7550, 7560, 7570, 7590, 7600,7610
101 2550, 2720, 2730, 2740, 2800, 2810,2820, 2880
II 270, 1120, 1210, 1620, 1640, 1650,1660, 1670, 1930, 1940, 1950, 3860,3870, 3880, 3970, 3980, 3990, 4000,4010, 4030, 4060, 5020, 5040, 5050,5170, 6430, 6440, 6450, 7660, 7670,7680
12 270, 1150, 1160, 1170, 1210, 1220,1230, 1960, 1970, 1980, 3030, 3040,3050, 3060, 3070, 3850, 3860, 3870,3880, 3960, 3970, 3980, 3990, 4000,4010, 4030, 4060, 5010, 5020, 5040,5050, 5170, 6460, 6470
13 1990, 2000, 2010, 6540, 6550, 6560
J 270, 1810, 1820, 1830, 3430, 3460,3490, 3520, 3900, 3910, 3920, 4030,4060, 4180, 4190, 4370, 4380, 5920,5930, 5940, 5960, 5970, 5980, 5990,7060, 7070, 7080, 7540, 7550, 7640
JB 15,0, 155C, 1580, 1680, 1690, 1710
44
Si u i |u 4
JG 1550, 1590, 1680, 1690, 1700, 1710, 1720
Ji 270, 3450, 3460, 3470, 3920, 3930,394Q, 3980, 3990, 4030, 4060, 4380,4390, 4400, 4420, 4430 1
J2 3910,ý 3920, 3930, '3940, 3980, 3990,4060, 4370, 4380, 4390, 4400, 4420,4430
J6 4360, 4400, 4410, 4430, 4440
J7 4350, 4360, 4400, 4410,'44B0, 4440
J8 4340, 4350, 4360
140, 200, 270, L650, 1770, 2200, 3420,3430, 3440, 3450, 3460, 3470, 3520,3620.,3660, 3670, 3680, 3730, 3740,3750, 3760, 3770,-3800, 3830, 3840,3870, 3880, 3900, 3930, 3940, 3950,3980, 3990, 4000, 4010, 4090, 4190,4200, 4210, 4220, 4240, 4250, 4260,4270, 4280, 4300, 4340, 4500, 4510,4520, 4530, 4540, 4550, 4810, 5210,5280, 5470, 5910, 5920o .6000, 6010,7420, 7640
KK 140, 200, 7420, 7430, 7640
KI 270, 3440, 3450, 3460, 3470, 3660,3730, 3740, 3770, 4200, 4240, 4250,4280
K2 3730, 3740, 3770, 4240, 4250, 4280
K8 3670, 3750, 3840, 4210, 4260, 4300,4340
45
K9 200, 3680, 3750, 3760, 4220, 4260,
4270
K22() 140, 200, 3870, 3880, 3930, 3940
K33() 140, 200, 3930, 3940, 3980, 3990,4000, 4010
L 3540, 3580, 3610, 4110, 4120, 4130,7360, 7420, 7460
Li 7500, 7510, 7520, 7560, 7600, 7660,
7710
L2 7550, 7560, 7600
M 3560, 4100, 4110, 4510, 4560, 4570,4620, 4630
N 3180, 3190, 4520, 4530, 4620, 4630,4960, 5090, 5510, 5220, 5260, 5500,5550, 6060, 6090, 6160
10 6510, 6520
NZ 1110, 1120, 1600, 1610
N1 590, 1020, 1110, 1150, 1420, 1600,1770, 1780, 1870, 1930, 1960, 1990,2270, 2350, 2590, 2780, 2790, 2B10,2900, 2950, 3180, 3210, 3230, 3400,3890, 3900, 3950, 4070, 4080, 6230,6250, 6520, 6710, 6830, 7010, 7020,7170, 7180, 7190, 7200, 7210, 7220,7390, 7490, 7740
N2 2950, 2960, 3190, 3320, 3330, 4180,4460, 4470, 4510, 4730
46
N3 4730, 4910, 5670, 587U, 5930, 5950,5960, 6300
N4 3400, 3410, 3680, 4220, 4500
NG 6820, 6830, 7010, 7020
NB 7480, 7500
N9 3230, 6250, 7490, 7500
P 4850, 4960, 4970, 5300, 5330, 5350,5360, 5400, 5420, 6060, 6090, 6100,611.0
P1 280, 1200, 1280, 1290, 1350, 1360,3320, 3330, 4520, 4530, 4620, 4630
PZ 4840, 4.850, 5260, 5500
P1 4600, 5180, 5550, 5560, 5590, 5830,6140, 6160, 6170, 6210
P2 190, 3610, 3840, 3900, 4080, 4090
P3 5550, 5560, 5590, 6150, 6160, 6200
P4 4870, 5190, 5310, 5460
R 6620, 6630
110 190, 1180, 1230, 1290, 1310, 1670,1680, 1690, 1800,' 1840, 2290, 2330,2610, 2620, 2640, 2710, 2760, 3020,3080, 3090, 5980, 5990, 6000, 6410,6480, 6850, 6860, 6870, 6890, (C980,
7040, 7080, 7090, 7230, 7240, 7510,7520, 7690, 7700
17
- -- - -
RAY(,) 150, 5380, 5390, 5440, 5450, 5730,6110, 6120, 6310
RAYI(,) 160, 2530, 2540, 2730, 2740, 2810,2820, 2890
RAY2(,) 170, 5330, 5340, 5360, 5370, 5670
Ri ].90, 1830, 1840, 1950, 2020, 3050,3090, 4470, 4480, 4490, 4550, 4580,4590, 4600, 4610, 4640, 4650, 4660,
K 4670, 4680, 4690, 6450, 6500, 7080,7090, 7570, 7580, 7670, 7680, 7690,7700
IR2 190, 1980, 2020, 3070, 4570, 4500,4590, 4600, 4610, 4640, 4650, 4660,4670, 4700, 4710, 6470, 6500, 7610,"7620
:R3 190, 2010, 2020, 6550, 6560
ST 2230, 2310, 2330, 2350
SU 7530, 7640, 7700
SZ 4520, 4580, 4600, 4620, 4640, 4660
S2 7640
S3 7630, 7640
T2 1200, 1280, 1290, 1300, 1350, 1360
W1(,) 130, 3270, 3320, 3360, 3460, 3470,3490, 3520, 3870
W2(,) 130, 3280, 3330, 3360, 3460, 3470,3490, 3520, 3880
48
UI__ _
x 1190, 1200, 2400, 2710, 2900, 2910'2920, 4390, 4410, 4420, 4440, 5050,5130, 5870, 6030, 6040, 6060, 6260,7190, 7250
XLAB() 150, 5700, 5740, 6300
XLAB1() 160, 2830, 2880, 6250
X0AB2() 170, 5640, 5670
XO 6860, 6890, 6940
XX(,) 140, 210, 1550, 1680, 1690
X1 6740, 6750, 6870, 6930, 6940
X2 6760, 6770, 6870, 6920, 6930
X3 6780, 6790, 6870, 6910, 6920
X4 6800, 6810, 6870, 6910
Y 1350, 2350, 2360, 2370, 2420, 2620
YLAB() 150, 5710, 5740, 6310
YLABI() 160, 2840, 2880, 6260
YLAB2() 170, 5650, 5670
YZ 6480, 6570, 6580, 6590, 6620, 6630
Y1 6490, 6570, 6630, 6640, 6750, 6870,6980
Y2 6500, 6580, 6640, 6650, 6770, 6880,6960, 6970
49
Y3 6560, 6590, 6650, 6790, 6880, 6950,6960
Y4 6810, 6880, 6950
zi 4580, 4680
Z2 4600, 4690
Z3 4640, 4700
Z4 4660,' 4710
50
GLOSSARY OF VARIABLESFOR
SIGNAL ANALYSIS PROGRAM(VARIABLE NAME AND DESCRIPTION)
VARIABLE DESCRIPTION
A Amplitude
ANSi The number of terrain points is equal to 2ANSIwhere 1 4 ANSI , 8.
ANS2 The length of the survey inte-rval ii feet, ANS2allows 4 places to the right of the decimal*point.
ANS3 The code for.type of input data is as follows:
0 for data equations1 for card reading
-1 for data equations
ANS4 The code for type of detrending is as follows:
1 for first to last point detrending2 for digital high pas filter3 for exponentially weighted
4 for no detrending
ANS5 The code for padding the array with Nl O's is:
1 for yes2 for no
ANS6 The code for interpolation is:
I for yes2 for no
ANS7 The code for amplitude smoothing is:
1 for yes2 for no
51
_ __" _ _ _
VARIABLE DESCRIPTION
ANS8 The code for GEO window is:
I for yes2 for no
Al(,) Storage array for terrain evaluation data.
A2(,) Storage array for torrain evaluation dataý
B1 Relative maximum and minimum profile values.
B2 Relative maximum and minimum profile values.
C The ordinate of the point AI(R,C).
CO The ordinate of the point Al(RO,CO).
Cl The ordinate of the point AI(Rl,CI).
C2 The ordinate of the point A2(R2,C2).
C3 The ordinate of the point Al(R3,C3).
E The quantity 36 divided by the length of thesurvey interval in feet.
F Frequency.
F1 The summation of the frequencies.
G Power spectral density.
GO() The coefficients of the GEO window.
IA The abscissa of the point Al(IA,IB)
IB The ordinate of the point AI(IAIB)
52
-_ -. . . " . ..
VARAIBLE DESCRIPTION
jThe abscissa of the point W J, K).
JB The abscissa of the point WI(JBJG).
JG !The ordinate of the point XX(JB,JG).
Ji 'ise upscisea of the point W1(jIK1) and ofAl(jI.,j2).
J6 The abscissa of the point A2(J6,J7).
V The ordinate of the point A2(j6,j7)
K The ordinate of the point WI(J,K)
K1 The ordinate of the point w2(J6,K7).
NI Number of terrain points.
N2 Number of terrain points divided by 2.
P period
PI 3.14159265
PZ 9999.99
P1 Root mean square.
P3 Area under pod.
P4 The summation of the power spectral densities.
R The abscissa of the point A1(R,C).
RO The abscissa of the point Al(RO.CO).
51
53 4ii.. __ __
VARIABLE DESCRIPTION
!RAY(,) Storage array for frequencies and psd's.
RAY1(,) Storage array for terrain points and maximumand minimum profile values.
RAY2(,) Storage array for periods and amplitudes.
R1 The abscissa of the point A2(Rl,Cl).
R2 The 3bscissa of the point A2(R2,C2).
R3 The abscissa of the point Al(R3,C3).
ST The surmnation of the values of the terrainpoint.
Wl(,) Stored values of (e-j) 2 /b/N
j ) 2 -r/NW2(,) Stored values of (e-)
X RMS from detrended zero mean terrain data.
XLAB() Storage for disruption "FREQUENCY" of x - axisused in graphics display.
XLABl() Storage for disruption !'DISTANCE" of x - axisused in graphics display.
XLAB2() Storage for disruption "PERXOD" of x - axis usedin graphics display.
XX(,) Terrain profile data arr.iy.
Y The value of the data equation; the average terrainpoint value.
YLAB() Storage for disruption "PSD" of y - axis usedin graphics display.
54
VARIABLE BRTON
YLAB2() Storage for disruption "AMPLITUDE" of y- axisused in graphics display.
I. A
-%V•III4
FLOWCHART VfOR SIGNA,, Aý4ALYSIS vROGrcAM
STMRT
PROGRAM FFT777 C INUT*75.OUTPUJT-75.TAPE*o-1l.STAPEI -OUTPUT&TAPE32* 12S.3E3US.AKIS1.1*.TAKU6-j0@)
47DIMENSION 0( .1a6U.~aSU.iU64.aa6iDIMENSION K2(2)oK33(2)*KK(72)vXX44j.1@)DIMENSION EYL~.LR1.L31DIMENSION NAY1(a.1").XtA3I(1),vLA31(1)DIMENSION A281)LAU1)YA()
INTEGER RCoRO.CO.,Rl*Cl*U*lC~m3.C3.PUVREAL Kaa.K33*K9oKKIDATA xx/410se./DATA Q0/-. 1476.-.1707#-. 1813to- 017&--IU?-,1707&-. 147V
CALL COMMCC 1UMI Q
CALL INITT(3"
56
ak
10 FONMT(IX.WEI3O if *O? I *s1.IId.& G A | , I A N I N WT I M I II O W NT fu o w - • l l l l 1 1
LN 0U.4.EU. L TO l-* .'.tZ.MU *
57
I I I 1 T I |-- I I I I I "1
1?0 FOMAT(MOMPAiVg INIVZL INI FUT ALLOWJ 4 PLACES PAST ISCINAL.
2" ,'.1X.~WOSENE 0 o*otCASK IGs
PWINT(1.USS)
220 FORMAT (lX, ENTER I FOR FIRST TO LAST POINT 3CTKN*INIWG.*..7X.* FOLR DIGITAL HIGH4 PASS FlLTl~~eU.%'.T31 P01 E)POONMIALLY UEIGHTED RU&H"INIM AQJENAQE#0s/.?X.4 FOR NO EINRS.4).AS
alAD *Asow
58
Ll1
PoIWVc Low4 I349 vGUNAT(1Lo mO mwUS THE mv .mub tvimgiYD.
VENTEJR 1 FOR YKS**.**41~o FOE .'IXAS
U162 FOR NosO../IX.UW
4OW FONNAT(IXo.30 YOU VWK UIPIITM WSooTjmNINSY.'IX.LOEMTK 1 FOR WS.v'./.sMOM POS 0W.%'.ImXvMIS? 6
S99
''V
CA L -00~
VITI(3. U..
U.SI Flloeo.T1•.a*.Psi PU@MI•*
X& ao14OFX6
0 44
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7 FSl 0-
* t€0~.u4o~'* F 'o'INT(( 4i-k. ),ISi)
ass A 1 (OO CO) -9. 6*01"t-pixpa. $*SU-•£•IN(Tj fig.,)&.u. 4Ils XC(-,).____62
A3(ROc.C@)'A1(fo.co)
_ __________________
62l
j
I1570 FONMT(IXo @THE FOLLOVINS DATA ROMTIW VM 0038 3.2
IF(Ag6SA.E@.)
F
I - ~t o
63
tole FT(IWJ8.) AS Iie bi~1 J
11-10 -D0-9 1645 01N-fi
11-10-XE -IF (AM94.G.8)
IIAI(O.C)-)(JUJQ
irCJGo T,. 10)~-
JO 1 6-4
Cl ~ ~ ~ ~ ~ ~ AW e1*ma. (J1 A) D 17 Ih~
RO-J-8ss6*CC-1) /CU:I4IMI'((18-1.).'356)
AlCRlC1 )-Al(ROCO) RS*13-M*e(C3-1)AI(IB.CB)o..*CAICRI.Cl)4Al(R3.C3))
CF
65
004
so im
FOWA(MOLATIE "IMM,&a 11111""IMMM IL VA~~u I____IM_______________ ___
RONIOROMC(*.I). *
LL
I34.A1 I(R0.o)o
RAVI1( (1. 101).0-1 X NE
I ~~RAVI M& 101 )-allLL~
67
I ~~~CALL QPL0Y(ftAYI.IO1.XLAII.3. aISl. *volt#1.1.IFO..0
1360 FOtfAT("/.1esX.*RMS FOW K UCTRE~ngEKD ZtR AN TERRAIN DATAK U?3.3,IX*IN M SO)
CI-1+KNT((Il-1. M) 73onn
L-
waJK-1* OWT(I-.El)/8E (s6)V (IKlma,
UIJRTE(Ze 19S0 )1,UI(JK ),W2(JK)K o$
KI"I
69
NoWN C(I - *ZT 6 )464'U5
I(KI-8KB+.T..5 17 ______-1
Id (J1I.J)mM1I1. E18)+K232)a179.l)AI II.113'K3(
AII11)mII1 Z)ilU
TF
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712Ftfli.LTcL,-& 3) .-. ib
,Ui
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L - -.
COON4
KI~~~K ea o o 1
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AU*W4DOl(S.?
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a )
72-J45
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OW(l1.CS mIot( 101)
03462400Kul -- O(.OF
&.S*cZ*oi(IIIOWE1.c")(3 04))I
Z3- 0 S(AI (on* oil Al C 10 CI).Ssz* ( AIl Mt#C)-AI (NJ CI))#&.S*CZ$ (AN(Ra 8.C3+A(m1*1.)) IIZ4 .St10(MR,(18.C)-4A1(#.CI 52O ).*Z(Ag(fts 08)+MtlNJCI )-
AI(RI.CI 1.21Al (R2.C2 )-23A2(R2,CZ).Z4
73
CALL NEMPM"e 70I0
L-+
846Foumy(/*rx,.AU .*.I. EULT8*.".1E#lX*9MOPLJTUU MEIOD
& FECO PCOO
pis**
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74
IFM S8Pt V(Zl.~j+S~ LT 1. 1.i-e~
28470 f-ale
A-UO~K~g75
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17
37" F OAATtoV.//.X*.UEiULTS UZI" WON OT F.P.To ANPLITUKcS*)
WmITE(j*Bh5WIP3'one FOOUT(.',PIX*ONM a .*F9.4#IK I1OHE$so/.1~X.AIE UNKE PSO
CALL NW
CALL 96EWAS+(Q
XLNW( I OM ID
CALL INITENIO
CCALL
CALL boU@WY
CALL HUMI*
COLL I IpASO
ZIHIT.T(~
CALL
CALL
CALL "OM~,
PRINT(1 8 60g or9830 FORMIYC,1.7X wwboom ANPtlIUs, USZWB G.C.O. ui,@ows,,al~. APLTUS(* .3N. OMIGO@*.VN.opuses 11K. PflS)
xIaK
-d30 31if Iu1.N3-K(3
8930 !F(J.LT*N3+*S)f) JOJ-40
T~
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coIIinZ?(1.aSSSM.P.-1 .0plt.2
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CALL EWOM-0
CALL NIT~c )-0-C
z
82
Tz
CALLl
CL i MS4)+
a3I
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1.41001-3
C.10 I((1-1* 1U
RI. I1-SM(C1-1)
C3411 . 00)
R3-13-856SCC3-1)V34A1 (Rt3,C3)CC2- .*Y8-YZ)-CCC3u(Y3-VZ-3XCC1)/S-CCa *-DO 3MM 1-4, A t3'IsS
Ao-I-sEG(C-1)Al(ft.C)uYZsI .S3UC1*.758CC2-.3?WSCC.3
YlovilYawY3
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I
I
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I
4
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co~zmccl-i. 15cow
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UN?(Iv~efty A (0.0
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"IS1 FOWMT(A4'/o1XoGF1IST TO LOST P@IlfT SCOW9DUINB%)
low Ioff(NI~Mp. )*I
T
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APPENDIX I
TERRAIN CHARACTERIZATION
BY
ZOLTAN J. JANOSI
SCIENCE & TECHNOLOGY DIVISIONU.S. ARMY TANK-AUTOMOTIVE RESEARCH & DEVELOPMENT LABORATORY
U.S. ARMY TANK-AUTOMOTIVE RESEARCH & DEVELOPMENT COMMAND
9191
r" •
TERRAIN CHARACTERIZATION
OBJECTIVE:
The objective of this research is to characterize randomterrain profiles by several parameters such as predominantfrequency (CPS) content as a function of vehicle velocity,power spectral density (PSD), frequency (CPF), PSD slope anda Odetrending parameter".
Additionally, natural terrain possesses a roll statisticor natural offset and research will be conducted to identifyit in terms of a vehicle's geometric properties and the auto-correlation function between terrain profiles which aredifferent but possess the same root-mean-square (RMS) level.
SCI ENTI FIC APPROACH:
There are many statistical methods for analyzing randomdata. This task will investigate the techniques developedfor time-dependent data and apply them to time-independentbut spatially dependent data to develop autocorrelationfunctions, root-mean-square values, and power-spectral-density plots for terrain profiles.
PROGRESS:
A. BACKGROUND
Investigations this year were focused on the analysisof terrain geometry by means of statistical techniques.The use of statistics is traditional and well documented inmany refinrences. A terrain profile as measured along a lineof finite distance is one sample record, y(x), A randomprocess is the collection (y(x)), of all sample records containedwithin the boundary of the terrain unit under investigation.
The validity of the statistical analysis depends on twoproperties exhibited by the random process: stationarityand ergodicity. To clarify this, assume the exitstence of afinite collection of sample records from a random process,and now examine the value of each sample record y(x) at somearbitrary point xl. The mean value of the random processat xI is:
NI(x1) Yk(xl).
-,}
This is also zalled the first moment. The correlation (calledthe autocorrelation function) between two points xI and xl + Ais defined as:
NRy(xl, xl + 4) Yk(xl) Yk(xl + I)-
I K= I
To be very rigorous, these expressions are valid only in the-limit as N - .The random process y(x1) is weakly stationaryif p (Xn) and R (xi x1 + A) are Invariant as xI varies overall I C .e., iy(xl, nd , x1 + A) aRn(A) for all
points x within the col ectionWof'san;le points. This meansthat the mean value of the elevation for the terrain unit isconstant and that the autocorrelation function is dependentonly on the separation distance between two points. Notethat if a is zero, then the square root of the autocorrelationfunction is the R14S of the terrain profile. In order for arandom process (y(x)) to be strongly stationary, all higherorder moments and joint moments for the autocorrelationfunction must be invariant with respect to the variable x.For many practical applications, a verification of weakstationarity justifies the assumption of strong stationarity.In any case, the collection of all higher order moments andjoint moments can be used to establish a complete familyof probability distribution functions that describe therandom process.
Consider the kth sample record Yk(x), The mean valueand autocorrelation function of kth sample record Is givenby:
X XPY•W Yk(x) dx and Ry(A,k) * l_ Yk (x) Yk(x + A) dxSX 0X 0
If the randum process (y(x)} is stationary, and i'y(k) andR (A,k) are constant for all values of k, then py(k) PyaMd R (A,k) Ry(a), and therefore the process is ergodic.Note 1hat only stationary random processes can be ergodic.
Therefore, if it is assumed that a terrain unit is arandom process that is both stationary and ergodic, then allthe necessary information can be obtained from one sampleterrain profile.
B. COMPUTATIONAL PROCEDURES:
Making these assumptions allows the statistical analysisof a single terrain profile to produce a root-mean-square
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roughness value and a power spectral density distributionplot which portray the characteristics of the terrain unitwhich is geographically associated with the sample. Thegeneral process is as follows:
1. Conduct a survey in the area for which-informationis required. Establish a path (not necessarily absolutelystraight) between 400 - 600 feet long and determine theelevation of the profile at one foot intervals.
2. Detrend the raw data by removing low frequencyinformation. Normally a cut off frequency of .0166 cycles/ftis used. (Detrending is discussed later).
3. Set the detrended profile to have a zero mean.
4. Calculate the autocorrelatlon function. The squareroot of the autocorrelation function with A equal to zerois the R1S of the profile.
5. Operate on the autocorrelation function usingFourier Transforms to yield raw power spectral densityestimates.
6, Apply smoothing coefficients and calculate thecentral frequency for each PSD estimate. (PSO is establishedfor a various frequency/band).
7. Graphic presentation.
Steps 2 through 6 have been written into a computerprogram, using basic language for a Wang 2200 series computer.Raw survey ddta are entered in a data block and the finishedproduct c:onsists of a listing of smoothed power spectraldensity estimates a, d associated center frequencies. Terrainprofiles up to 699 feet long may be processed, with up to200 autocorrelation coefficients. At the operator'sdiscretion, any one of four methods of detrending may be usedor he may ignore detrending.
Steps 3, 4, 5, and 6 are well documented in manyreferences. All authorities agree, so there is little needfor discussion. However, Step 2, detrending, is not asclear cut. There are several techniques available, noneof which are ideal. However, detrending is importantbecause it drastically alters the RMS value and the shapeof the PSD plot. It is necessary because of the statisticalnature of the data reduction process. In order for the
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process to identify all frequencies which are present, thesample record must be several times longer than the wavelength of the lowest frequency. Since the frequency contentis unknown, all frequencies below a certain limit must beeliminated and a sample record length several times longerthan the wave length of the cut off frequency must be used.If the removal of long wave length information, or a netchange in elevation, is not accomplished, the reduction
* process will distribute the associated "power" throughoutthe entire spectrum of the PSD plot. Furthermore, if anet change in elevation does occur, it will invalidate theassumption of ergodicity. This, of course, destroys thevalue of the analysis.
Detrending is often called filtering. The type offilter which is of interest in terrain profile analysiswould be a high pass filter; i.e., those frequencies lowerthan the cut off frequency are filtered out and thoseabove the cut off frequency are passed. Unfortunately,there are no ideal mathematical filters; no mathematicaldata manipulation will entirely eliminate the frequencieslower than the limit and leave the higher frequenciesunchanged. There is always some distortion of Informationon the pass side of the filter and some passing ofinformation on the filter side. The best that can be doneis to look for the filter with the sharpest possible cutoff characteristics and minimal distortion on the psH
side. Much nf the effort in FY76 was directed to this end.Several filtering techniques were investigated but onlytwo proved to be promising.
One such numerical filter is known as the runningaverage. It is a two sided filter that detrends withouta phase shift and is able to remove linear trends as wellas long wave length information. The filter calculatesa correction factor for each point in tfr survey. Thecorrection factor 'is then subtracted from the value ofeach survey point to yield a corrected value. The seriesof corrected values forms a new "detrended" profile devoidof long wave length information. The correction factorfor each survey point is calculated by summing the eleva-tions at a given number of points ahead of and behindthe point to be detrended, plus the value of the pointitself and dividing the sum by the total number of points.The mathematical expressions are as follows:
95
Lf
tI
k-t/2 z/2ym) - x + VAX); K +-' (- " 1),kI+ L 2 2
L
2
where:
YM(X) the correction factor to be subtractedfrom the ordinate of the surveyed point
a• * number of survey points
.-AX length of running average
y(X) * value of any point in. the original survey
X- horizontal distance
AX- measurement interval
"- Note than the raw values are used throughout the process. Thepreviously corrected values are ignored during detrending.The detrended profile is generated by:
T (x) y(X) - y,(x)
where:
Y(X) - the ordinate of the detrended survey point. ThisSechnique generates a unique correction factor for each surveypint.
The cut Off frequency of this filter is controlled bythe number of survey points and measurement interval includedin the averaging. For example, if the survey interval is onefoot and the filter looks ahead and behind 30 points, then'the cut off frequency is approximately .0166 cycles/ft(corresponding to a 60 foot length). The error functionconcerning this process Is:
6() 1 -2 sin (a D/2)9D
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l-
where:
D a (t + ])A X
. = number terms for averaging
AX -. survey Interval
Q -frequency
Figure 1 shows a plot of the error function for filterswhich look ahead and behind 33, 50, and 70 survey points.It shows that the filters have sharp cut off characteristicsbut that they also distort frequency amplitudes in the passside of the filter. For each error function shown, thefirst zero error point occurs very nearly at the frequencywhose wave length is equal to the length of the running average.Thereafter, the filter alternately over and under estimatesthe amplitudes. The maximum over estimation Is almost 50%;the maximum under estimation is a little more than 20%.However, the decay characteristic quickly reduces the dis-tortion to + a few percent.
The second filter, introduced by Van Deusen, is amodification of the running average. It is termed a "movingtwo sided exponentially weighted average." A correctionfactor is calculated in the same manner except that thevalues used in the calculation are weighted proportionallyto their distance from the point being detrended. The moredistant points are less influential than nearby points.The weighting is accomplished by an exponential factor.Mathematically the filter expression is:
E
I (y(X + i.Ax) + y(X - A.AX)) exp(-_L.AX)Yn(X) - 0
It itR .. . .
! exp(-IL0
where: y(X) elevation at the point X
Yn(X) a correction factor
L - step number
aX w measurement interval
A- weighting constant
then:97
El -
V(X) y(X) - Yn(X)where:
Y(X) - value of detrended profile point.
Lamda is an independent variable which is chosen toestablish the cut off frequency. Then in actual computation,a limit on the value of the exponent is set that causes Lto be limited to some finite number C. Van Deusen chose tocut off computation when the absolute value of the exponentexceeded 3. By adjusting the value of lamda and the limiton the value of the exponent, filter" characteristics can bemodified over a wide range. If values are assigned whichcause a rapid decline in the value of the survey pointsused in computing Y(X), the error function will exhibit ageneral under estiwation of amplitudes in the pass sideof the filter. An example of this phenomenon of weightingis shown in Figure 2 for three different values of Lamda.
The considerable effort was directed at investigatingthe weighting constant and its effect on optimizing filtercharacteristics. The result is an improved filter whichhas better cut off characteristics and limits distortionin the pass side of the filter to less than 10%. Theerror function is shown in Figure 3. The summation of termsfor averaging is stopped when the absolute value of theexponent exceeds 1.2 with Lamda w 30. The filter parameterswere chosen to less severely depress the values of thesurvey points in computing Y(X). Note that some of theoscillatory characteristics of the straight runningaverage error function are evident. This improved fllterhas been incorporated in the PSO computer program and isregularly' used for detrending field survey data.
The most noticable effect of detrending techniquesoccurs in the calculation of the RMS value of a profile.Even slight changes can cause large variations in theRMS value. If we wish to be very precise, then even theimproved filter cannot stand alone because it does passsome low frequency information which ideally it shouldnot. Additional filtering can be done graphically onthe final plot of the PSD. The square root of the areaunder the PSD plot is the RNS of the profile. By sub-tracting the area in the low frequency end of the plotfrom the total area, the profile can be further detrended.This combination of numerical and graphical filteringproduces RMS values as close to the true values aspossible with the statistical analysis technique.
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FUTURE PLANS:As a result of the work described here, a computer program
is available that produces RtS and PSD data from terrain profilesurvey data. The procedure uses an improved mathematicalfilter to eliminate undesirable wave lengths and slopes.It also smoothes the PSD plots by reducing the side lobeswhich occur due to the limited length of the surveyed profile.
The procedure is based on the Wiener-Khinchin equationwhich states that the PSD is the Fourier transform of theautocorrelation function. Hence, one calculates theautocorrelation function first. (The practical applicationwas first published by Blackman and Tukey).
However, a more direct approach, the computation of theFourier transform of the profile itself, is now a practicalproposition because a new, faster computational method hasbeen developed for the performance of Fourier transformcalculations.
It is, therefore, recommended that the application ofthe Fast Fourier Transform method to terrain profile analysisbe undertaken next.
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_NCTION FOR RUNNING
AVERAGE DETREI1D ING
I ,-
1.0
I'I
+±70
.1+ 566-1/2""•
+33
.01 I ..005 .01 .1 .5
FREQ. CYc.IFT.
FIGURE 1
100IO0 1
MOVING TWO SIDED
EXPONENTIALLY WEIGHTED AVERAGEFILTER GAIN WEIGHTING CONSTANT CUT OFF AT SxY/L>3
1.0
.01.005 .01 .0166
FpR•Q., CYc./FT.
'1o••GURE 2
J-
" - MOVIdG TWO SIDED
EXPONENTIALLY WEIGHTED AVERAGE
FILTER GAIN WEIGHTING CONSTANT CUT OFF AT SxY/L>1.2
1.0
Ii/g I
I .1 4-=- --
.005 .01 .016 .10
FREQ., CYC/FT.FI'- .05 O .1 ,1 .
.. . . . ... . . . . .. . . ..... ....•... ......
S ] DISIRIBUTION LIST
Commanding GeneralU. S. Army Tank-Automotive
Research and Development CommandWarren, Michigan 48090
Attention: Library Services Division c3 copies)DRDTA-LUL
Tank-Automoti ve ConceptsLaboratory (TACL)
DRDTA-Z (20 copies)
] DirectorDefense Documentation CenterCameron StationAlexandria, VA 22314 (12 copies)
I11[
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SECURITY CLASSIFICATION 07 THIS PAGE (Mim Deta Entered)
REPORT DOCUMENTATION PAGE READ rNSTUCTIONSBEFORE COMPLETING FORM
1. REPORT NUMBER 2. GOVT ACCESSION No. 3. RECIPIENT'S CAALOG MUMIER
12412 -4. TITLE (and Subtitl,) S. TYPE OF REPORT I PERIOD COVERED
TARADCOM SIGNAL ANALYSIS PROGRAM Final Technical Report4/78-9/78
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G.A. FIX
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASKSurvival Technology Function AREA & WORK UNT NUMBERSTarviAl Concepts Laboratory R OU U
Warren, MI 48090 lLI61101A91AII. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATEUS Army Tank-Automotive Research and September 1978Development Command, DRDTA-Z IS. NUMBER OF PAGESWarren, MI 48090. 105I4 MONITORING AGENCY NAME & ADORESS(If dilferent from Controlling Office) IS. SECURITY CLASS. (of this tarport)
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SCHEDULEIS. DISTRIBUTION STATEMENT (of this Report)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, If dli erua from Report)
14. SUPPLEMENTARY NOTES
IS. KEY WORDS (Continue on reverse aid& If necewo , aid Identify by block number)
Fast Fourier Transform, Signal Analysis
20. ANSTNACT (GartAN ,.am f eLw "1r If ereN MW 04wuittf by block nuinbeu')5The objective of this report is to provide a user manual for theSignal Analysis Computer Program.
The TARADCOM Signal Analysis Program (formerly called the FastFourier Transform Program) was developed originally as a BASIC
Wang Program by Robert Daigle and associates. The TSA computerrogram has been converted from BASIC to FORTRAN and various graphi
SFORM AeDO ••, 473 t~oor MO~nO•OUTZ UNCLASSIFIED "'""
114SECuPTY CLASSIFICATIOP, OF T-HS PAGE (Wire, Data Entered)..
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>displays, such as linear plot of evaluation vs. distance, a pointplot of amplitude vs. periods, and a log-log graph of powerspectral density vs. frequency, have boen added.
Terrain data input to the program may be used in processing,rather than date equations that are contained in the program.options available during processing include: first to last pointdetrending, digital high pass filters, exponentially weightedrunning average, no detrending, interpolation, amplitude smoothing,and a GEO window. The results of the TSAP include, besidesgraphics displays, amplitudes, periods, frequencies, power spectraldensities, and RMS values.
UNCLASSIFIED10 5 ,ECUNVY CLA-•IICATION Of THIS PA,(Wnu Doe. Sn•,mhQ I •
